Storage systems are often configured to include multiple storage tiers, with different ones of the tiers providing different levels of input-output (IO) performance or other characteristics. In such systems, data may be moved from one tier to another within a given storage system based on access frequency of the data or other factors. However, conventional storage tiering arrangements can be unduly inflexible when implemented in a storage system that comprises a parallel file system. For example, transfer of large files or other types of data objects between storage tiers of such a storage system can be inefficient and potentially wasteful of storage system resources under certain conditions.